14 1. Differential Equations Figure 1.6-1: A demonstration of the use of the MyAnimate command for a function of one spatial and one temporal variable. MyAnimate[f_, {x,x0_,x1_}, {y,y0_,y1_}, {z,z0_,z1_}, {t,t0_,t1_}, n_] := ListAnimate[Table[Plot3D[f, {x, x0, x1}, {y, y0, y1}, PlotRange - {z0, z1}], {t, t0, t1, (t1 - t0)/n}]] To use the command to animate a function f(x, t) of one spatial and one temporal variable, you choose a viewing window (x0 ≤ x ≤ x1, y0 ≤ y ≤ y1) and a time interval (t0 ≤ t ≤ t1) and determine the number of frames you want (n) with the understanding that more frames produce a smoother movie but also require more computer power. The command MyAnimate[f[x,t],{x,x0,x1},{y,y0,y1},{t,t0,t1},n] should then produce the desired animation. Similarly, for a func- tion f(x, y, t) with two spatial variables, one can graph an animated surface by saying MyAnimate[f[x,y,t],{x,x0,x1},{y,y0,y1},{z,z0,z1}, {t,t0,t1},n] where the three-dimensional viewing “box” is specified by the inter- vals in x, y and z. Some homework questions below will give you an opportunity to test your ability to use these commands.

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2010 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.